Dynamics of Small Neural PopulationsAmerican Mathematical Soc., 1996 - 125 pagina's This book arose from a series of lectures presented at the CRM Summer School in Mathematical Biology held at the University of British Columbia in the summer of 19934 by John Milton, a clinical neurologist and biomathematician. In this work, three themes are explored: time-delayed feedback control, noise, and statistical properties of neurons and large neural populations. This volume focuses on systems composed of 2-3 neurons. Such neural populations are small enough to permit experimental manipulation while at the same time being well enough characterized so that plausible mathematical models can be posed. Thus direct comparisons between theory and observation are in principle possible. |
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action potential amplitude Aoff Aref arise asymptotic asymptotic stability basket cell CA3 neuron chaos chaotic Chapter complex constriction cortex coupled map lattices delay delay differential equation density described differential equation dynamical systems effects of noise example excitatory experimental Fitzhugh-Nagumo equations fluctuations frequency function GABA hence hippocampal histograms Hopf bifurcation input-output relation integrate and fire ISI histograms light reflex clamped limit cycle M-H model mechanisms membrane potential msec muscle negative feedback nervous system neural activity neural network neural populations neural spike train neuron fires noise intensity noisy input nonlinear number of neurons observed obtain occur onset oscillations parameters PCNF period Poisson process possible predicted pupil area pupil cycling pupil light reflex pupillary receptors recurrent inhibitory loop relative refractory retina Schematic representation shown in Figure solutions of 6.3 spatial spiral waves spreading depression squid axon stability Stochastic resonance synaptic threshold values variables wave phenomena
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Pagina ix - ... particular, I should have investigated why we attribute three dimensions to space. I may be pardoned then for taking up again these important questions. Is mathematical analysis then, whose principal object is the study of these empty frames, only a vain play of the mind ? It can give to the physicist only a convenient language ; is this not a mediocre service, which, strictly speaking, could be done without; and even is it not to be feared that this artificial language may be a veil interposed...
Pagina ix - Far from it; without this language most of the intimate analogies of things would have remained forever unknown to us ; and we should forever have been ignorant of the internal harmony of the world, which is, we shall see, the only true objective reality. The best expression of this harmony is law. Law is one of the most recent conquests of the human mind; there still are people who live in the presence of a perpetual miracle and are not astonished at it. On the contrary, we it is who should be astonished...
Pagina ix - ... qualitative space"; in particular, I should have investigated why we attribute three dimensions to space. I may be pardoned then for taking up again these important questions. Is mathematical analysis, then, whose principal object is the study of these empty frames, only a vain play of the mind? It can give to the physicist only a convenient language; is this not a mediocre service, which, strictly speaking, could be done without; and even is it not to be feared that this artificial language...